Pre-Publicación 2025-01
Boumediene Chentouf, Sabeur Mansouri, Mauricio Sepúlveda, Rodrigo Véjar:
Theoretical and numerical results for the exponential stability of the rotating disk-beam system with a boundary infinite memory of type angular velocity
Abstract:
This paper is concerned with the investigation of the effect of a boundary infinite memory term on the stability of the rotating disk-beam system. Assuming the infinite memory is of angular velocity type, the minimal state approach is employed to handle the memory term. Under specific conditions on the memory kernel function, we demonstrate that the problem is well-posed and its solutions are exponentially stable. Notably, the beam’s vibrations are suppressed, and the disk achieves a desired angular velocity provided the latter remains bounded. Using the Finite Volumes Method, a comprehensive numerical study validates the theoretical stability results.
